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  • Aim: What is the Law of Sines and how can we apply it? (This formula is on your Regents Reference Sheet)


At the end of this lesson, you will be able to...
  1. express the Law of Sines in different forms
  2. explain the conditions necessary to apply the Law of Sines
  3. apply the Law of Sines to find the length of a side of a triangle, if measures are given for two angles and a side
  4. justify whether or not a triangle is acute, obtuse or right
  5. solve problems involving the use of the Law of Sines

The Law of Sines is a formula that allows you to find the missing sides or angles from a triangle.

Copy the questions into your notebook and answer them as you watch the video.

  1. What is the formula for the Law of Sines?
  2. How many ratios do you need to use to solve for a missing part of a triangle?
  3. What is an oblique triangle?
  4. What are the requirements to solve this type of triangle?
  5. What relationships are we using today?
  6. Which one did James say was going to be discussed in another video?


Video 1


Video 2


As you've seen in both videos, you can solve for the variable first as in Video 1, or you may use cross-products to solve as in Video 2.


  • Classwork: Solve each problem. Be sure to follow directions. Draw a picture for each.

1. In triangle ABC, c= 12, the measure of angle B = 120, and the measure of angle C = 45. Find the exact value of side b.
(Side b = 6sqrt6)

2. In triangle DEF, the measure of angle D = 50, the measure of angle E = 95, and f = 12.6. Find d to the nearest tenth.
(side d= 16.8)


  • Homework: #3-21 odd

Law_of_Sines_1.JPG

Law_of_Sines_2.JPG

  • Answers

A-Law_of_Sines.JPG

  • Journal entry: Ptolemy was aware of the Law of Sines in the 2nd century BC. Use the Internet to find out how the Greeks used this theorem.